To find the solution to the given system of linear equations, we will solve the equations simultaneously.

Step 1: Write the equations
The given system of linear equations is:
2x - y = 6 ----(1)
4x + 5y = 16 ----(2)

Step 2: Solve the equations simultaneously
To solve the equations simultaneously, we can use the method of substitution or elimination. Let's solve it using the method of substitution:

From equation (1), we can express y in terms of x:
y = 2x - 6

Substitute this value of y in equation (2):
4x + 5(2x - 6) = 16

Simplify the equation:
4x + 10x - 30 = 16
14x - 30 = 16

Add 30 to both sides of the equation:
14x - 30 + 30 = 16 + 30
14x = 46

Divide both sides of the equation by 14:
14x/14 = 46/14
x = 46/14
x = 23/7

Step 3: Substitute the value of x in either of the original equations to find the value of y.
Let's substitute the value of x in equation (1):
2(23/7) - y = 6

Simplify the equation:
46/7 - y = 6

To eliminate the denominator, multiply both sides of the equation by 7:
7(46/7 - y) = 7(6)
46 - 7y = 42

Subtract 46 from both sides of the equation:
46 - 46 - 7y = 42 - 46
-7y = -4

Divide both sides of the equation by -7:
-7y/-7 = -4/-7
y = 4/7

So, the solution to the system of linear equations is x = 23/7 and y = 4/7.

Step 4: Check the solution
To verify the solution, substitute the values of x and y in both equations:
Equation (1): 2(23/7) - 4/7 = 6
Equation (2): 4(23/7) + 5(4/7) = 16

Both equations should be satisfied by the values of x and y.

Upon calculation, we find that both equations are true when x = 23/7 and y = 4/7.

Therefore, the correct answer is option B: (-1,4).